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Planform evolution in convection–an embedded centre manifold

Published online by Cambridge University Press:  17 February 2009

A. J. Roberts
A. J. Roberts
Affiliation:
Dept. of Applied Math., The University of Adelaide, Adelaide 5001, South Australia.
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Abstract

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The new motion of embedding a centre manifold in some higher-dimensional manifold leads to a practical approach to the rational low-dimensional approximation of a wide class of dynamical systems; it also provides a simple geometric picture for these approximations. In particular, I consider the problem of finding an approximate, but accurate, description of the evolution of a two-dimensional planform of convection. Inspired by a simple example, the straightforward adiabatic iteration is proposed to estimate an embedding manifold and arguments are presented for its effectiveness. Upon applying the procedure to a model convective planform problem I find that the resulting approximations perform remarkably well–much better than the traditional Swift-Hohenberg approximation for planform evolution.

Type
Research Article
Information
The ANZIAM Journal , Volume 34 , Issue 2 , October 1992 , pp. 174 - 198
Copyright
Copyright © Australian Mathematical Society 1992

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